if a man is a hetero zygote for a trait but the woman is homozygous recessive, what are the chances that their children will be homozygous dominant

To understand the chances of their children being homozygous dominant, we need to have some basic knowledge of genetics and how traits are inherited.

In this scenario, the man is heterozygous (or a carrier) for the trait, while the woman is homozygous recessive. Let's use the letter "A" to represent the dominant allele and "a" for the recessive allele.

The possible genotypes for the man could be: Aa (heterozygous) or aa (homozygous recessive).
The possible genotypes for the woman would be: aa (homozygous recessive).

When these two individuals have children, each parent will randomly contribute one allele to their offspring. So, let's consider the possible combinations when the man and woman have children:

1. If the man contributes the dominant allele "A" and the woman contributes the recessive allele "a", the child would be heterozygous (Aa) for the trait.

2. If the man contributes the recessive allele "a" and the woman contributes the recessive allele "a", the child would be homozygous recessive (aa) for the trait.

So, in this particular case, there are no chances of the children being homozygous dominant (AA) because neither parent possesses the dominant homozygous genotype (AA).

Therefore, based on the given information, the probability of their children being homozygous dominant is zero.